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 A292163 a(n) is the least prime p such that the orderly concatenation of the n successive powers of p yields a prime number; a(n)=0 if n is a multiple of 6. 0
 3, 3, 337, 23, 0, 373, 37, 839, 421, 7, 0, 1447, 2113, 29, 43, 17, 0, 1789, 523, 84737, 7669, 397, 0, 3851, 3583, 99149, 146023, 157, 0, 14173, 38329, 1229, 8017, 1021, 0, 18979, 5437, 17207, 6571, 47, 0, 347, 43669, 25847, 257353, 2887, 0, 33889, 71287 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS See in the Prime Puzzle link the discussion for when n is a multiple of 6. LINKS Carlos Rivera, Puzzle 892. Primes as a concatenation of a series of powers of a prime, The Prime Puzzles and Problems Connection. EXAMPLE For n=2, the concatenation of 3^0 and 3^1 is 13 which is prime (while 12 was not prime); so a(2) = 3. For n=3, the concatenation of 3^0, 3^1 and 3^2 is 139 which is prime (while 124 was not prime); so a(3) = 3. MAPLE g:= proc(p, n) local i, t;   t:= p^(n-1):   for i from n-2 to 0 by -1 do     t:= t + 10^(1+ilog10(t))*p^i   od;   t end proc: f:= proc(n)   local p;   if n mod 6 = 0 then return 0 fi;   p:= 3;   while not isprime(g(p, n)) do     p:= nextprime(p);     if n mod 3 = 0 then while p mod 3 = 1 do p:= nextprime(p) od fi:   od;   p end proc: map(f, [\$2..30]); # Robert Israel, Sep 10 2017 PROG (PARI) pconc(p, n) = {my(s = "1"); for (k=1, n, s = concat(s, Str(p^k)); ); eval(s); } a(n) = {if (!(n % 6), return (0)); n --; my(p = 2); while (! isprime(pconc(p, n)), p = nextprime(p+1)); p; } CROSSREFS Cf. A047253. Sequence in context: A007301 A009715 A335258 * A242886 A221947 A138662 Adjacent sequences:  A292160 A292161 A292162 * A292164 A292165 A292166 KEYWORD nonn,base AUTHOR Michel Marcus, Sep 10 2017 EXTENSIONS a(27)-a(50) from Robert Israel, Sep 10 2017 STATUS approved

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Last modified September 23 03:04 EDT 2020. Contains 337291 sequences. (Running on oeis4.)